MinT - Best Known (253−159, 253, s)-Nets in Base 4

Best Known (253−159, 253, s)-Nets in Base 4

(253−159, 253, 104)-Net over F₄ — Constructive and digital

Digital (94, 253, 104)-net over F₄, using

t-expansion [i] based on digital (73, 253, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(253−159, 253, 144)-Net over F₄ — Digital

Digital (94, 253, 144)-net over F₄, using

t-expansion [i] based on digital (91, 253, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(253−159, 253, 775)-Net in Base 4 — Upper bound on s

There is no (94, 253, 776)-net in base 4, because

1 times m-reduction [i] would yield (94, 252, 776)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 54 618690 753436 254549 458866 485454 753949 486508 877496 268529 723534 040325 508883 331430 394721 268360 376210 901218 505963 865585 238139 185353 331047 800477 766504 793248 > 4²⁵² [i]