MinT - Best Known (48−39, 48, s)-Nets in Base 256

Best Known (48−39, 48, s)-Nets in Base 256

(48−39, 48, 266)-Net over F₂₅₆ — Constructive and digital

Digital (9, 48, 266)-net over F₂₅₆, using

net from sequence [i] based on digital (9, 265)-sequence over F₂₅₆, using
- Niederreiter sequence [i]

(48−39, 48, 513)-Net over F₂₅₆ — Digital

Digital (9, 48, 513)-net over F₂₅₆, using

t-expansion [i] based on digital (8, 48, 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]

(48−39, 48, 28168)-Net in Base 256 — Upper bound on s

There is no (9, 48, 28169)-net in base 256, because

1 times m-reduction [i] would yield (9, 47, 28169)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 153986 835631 206468 715788 863506 170368 845049 748727 024061 108681 047884 614606 652589 631593 883690 591880 943870 830484 301056 > 256⁴⁷ [i]