MinT - Best Known (26, 77, s)-Nets in Base 128

Best Known (26, 77, s)-Nets in Base 128

(26, 77, 288)-Net over F₁₂₈ — Constructive and digital

Digital (26, 77, 288)-net over F₁₂₈, using

t-expansion [i] based on digital (9, 77, 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]

(26, 77, 513)-Net over F₁₂₈ — Digital

Digital (26, 77, 513)-net over F₁₂₈, using

t-expansion [i] based on digital (24, 77, 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]

(26, 77, 204039)-Net in Base 128 — Upper bound on s

There is no (26, 77, 204040)-net in base 128, because

1 times m-reduction [i] would yield (26, 76, 204040)-net in base 128, but
- the generalized Rao bound for nets shows that 128^mÂ â‰¥ 14059 802097 055568 880328 018718 425960 432003 269940 198692 230726 653802 011942 948775 368698 312904 621875 987821 099190 017505 361679 780601 782087 493906 339687 131973 536044 484960 > 128⁷⁶ [i]