MinT - Best Known (24, 56, s)-Nets in Base 128

Best Known (24, 56, s)-Nets in Base 128

(24, 56, 408)-Net over F₁₂₈ — Constructive and digital

Digital (24, 56, 408)-net over F₁₂₈, using

(u,Â u+v)-construction [i] based on
1. digital (3, 19, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]
2. digital (5, 37, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(24, 56, 515)-Net in Base 128 — Constructive

(24, 56, 515)-net in base 128, using

base change [i] based on digital (17, 49, 515)-net over F₂₅₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 16, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]
  2. digital (1, 33, 258)-net over F₂₅₆, using
    - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
      - Niederreiter sequence [i]

(24, 56, 642)-Net over F₁₂₈ — Digital

Digital (24, 56, 642)-net over F₁₂₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(24, 56, 1270478)-Net in Base 128 — Upper bound on s

There is no (24, 56, 1270479)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 10086 988021 990797 800614 701347 109680 689025 669057 144074 550339 786594 999187 277137 097479 333568 488624 086275 085747 840969 334028 > 128⁵⁶ [i]