MinT - Best Known (15, 15+37, s)-Nets in Base 256

Best Known (15, 15+37, s)-Nets in Base 256

(15, 15+37, 272)-Net over F₂₅₆ — Constructive and digital

Digital (15, 52, 272)-net over F₂₅₆, using

net from sequence [i] based on digital (15, 271)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(15, 15+37, 513)-Net over F₂₅₆ — Digital

Digital (15, 52, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 52, 513)-net over F₂₅₆, using
- net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
    - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

(15, 15+37, 197204)-Net in Base 256 — Upper bound on s

There is no (15, 52, 197205)-net in base 256, because

1 times m-reduction [i] would yield (15, 51, 197205)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 661 065595 562519 010407 256522 465096 288384 452318 323853 303186 165988 054029 057315 888623 844396 741760 637327 832129 040032 771537 768326 > 256⁵¹ [i]