MinT - Best Known (130−94, 130, s)-Nets in Base 16

Best Known (130−94, 130, s)-Nets in Base 16

(130−94, 130, 65)-Net over F₁₆ — Constructive and digital

Digital (36, 130, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 130, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(130−94, 130, 104)-Net in Base 16 — Constructive

(36, 130, 104)-net in base 16, using

t-expansion [i] based on (35, 130, 104)-net in base 16, using
- base change [i] based on digital (9, 104, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(130−94, 130, 193)-Net over F₁₆ — Digital

Digital (36, 130, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 130, 193)-net over F₁₆, using
- net from sequence [i] based on digital (33, 192)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 33 and N(F) ≥ 193, using
    - a curve from the manYPoints database [i]

(130−94, 130, 2595)-Net in Base 16 — Upper bound on s

There is no (36, 130, 2596)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 3 466538 242288 928382 881294 541878 539438 164272 160853 663405 927371 082813 910368 203745 047799 278213 098392 122469 390390 971245 049718 498544 519102 683226 293770 555421 142656 > 16¹³⁰ [i]