MinT - Best Known (74−49, 74, s)-Nets in Base 128

Best Known (74−49, 74, s)-Nets in Base 128

(74−49, 74, 288)-Net over F₁₂₈ — Constructive and digital

Digital (25, 74, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 74, 288)-net over F₁₂₈, using
- net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
    - a function field by SÃ©mirat [i]

(74−49, 74, 513)-Net over F₁₂₈ — Digital

Digital (25, 74, 513)-net over F₁₂₈, using

t-expansion [i] based on digital (24, 74, 513)-net over F₁₂₈, using
- net from sequence [i] based on digital (24, 512)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 24 and N(F) ≥ 513, using
    - a curve from the manYPoints database [i]

(74−49, 74, 198136)-Net in Base 128 — Upper bound on s

There is no (25, 74, 198137)-net in base 128, because

1 times m-reduction [i] would yield (25, 73, 198137)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 6704 594297 757966 859453 615987 458383 348750 621706 687136 029327 074866 857685 809984 231209 713593 309815 898387 456370 460671 135902 658134 010662 764572 079654 991745 898663 > 128⁷³ [i]