MinT - Best Known (19, 19+47, s)-Nets in Base 256

Best Known (19, 19+47, s)-Nets in Base 256

(19, 19+47, 276)-Net over F₂₅₆ — Constructive and digital

Digital (19, 66, 276)-net over F₂₅₆, using

net from sequence [i] based on digital (19, 275)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(19, 19+47, 513)-Net over F₂₅₆ — Digital

Digital (19, 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]

(19, 19+47, 236478)-Net in Base 256 — Upper bound on s

There is no (19, 66, 236479)-net in base 256, because

1 times m-reduction [i] would yield (19, 65, 236479)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 3 432633 974392 610110 574409 268728 497782 897164 709651 873697 226466 090397 127557 734254 009168 033311 530595 151211 803229 263551 525644 154384 136781 337272 276794 672863 161336 > 256⁶⁵ [i]