MinT - Best Known (32−28, 32, s)-Nets in Base 128

Best Known (32−28, 32, s)-Nets in Base 128

(32−28, 32, 192)-Net over F₁₂₈ — Constructive and digital

Digital (4, 32, 192)-net over F₁₂₈, using

t-expansion [i] based on digital (3, 32, 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]

(32−28, 32, 215)-Net over F₁₂₈ — Digital

Digital (4, 32, 215)-net over F₁₂₈, using

net from sequence [i] based on digital (4, 214)-sequence over F₁₂₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 4 and N(F) ≥ 215, using
  - a curve from the manYPoints database [i]

(32−28, 32, 257)-Net in Base 128 — Constructive

(4, 32, 257)-net in base 128, using

base change [i] based on digital (0, 28, 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]

(32−28, 32, 3113)-Net in Base 128 — Upper bound on s

There is no (4, 32, 3114)-net in base 128, because

the generalized Rao bound for nets shows that 128^mÂ â‰¥ 27 051516 737125 646447 356678 780506 657095 568544 735128 629673 563418 555536 > 128³² [i]