MinT - Best Known (13, 66, s)-Nets in Base 256

Best Known (13, 66, s)-Nets in Base 256

(13, 66, 270)-Net over F₂₅₆ — Constructive and digital

Digital (13, 66, 270)-net over F₂₅₆, using

net from sequence [i] based on digital (13, 269)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(13, 66, 513)-Net over F₂₅₆ — Digital

Digital (13, 66, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 66, 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]

(13, 66, 43373)-Net in Base 256 — Upper bound on s

There is no (13, 66, 43374)-net in base 256, because

1 times m-reduction [i] would yield (13, 65, 43374)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 432986 245521 676047 750082 636348 345582 864135 349478 560318 429163 930824 802962 555381 994552 799185 629530 760333 686966 058716 019281 687502 209080 488322 474659 032414 678996 > 256⁶⁵ [i]