MinT - Best Known (91, 91+161, s)-Nets in Base 4

Best Known (91, 91+161, s)-Nets in Base 4

(91, 91+161, 104)-Net over F₄ — Constructive and digital

Digital (91, 252, 104)-net over F₄, using

t-expansion [i] based on digital (73, 252, 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]

(91, 91+161, 144)-Net over F₄ — Digital

Digital (91, 252, 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]

(91, 91+161, 725)-Net in Base 4 — Upper bound on s

There is no (91, 252, 726)-net in base 4, because

1 times m-reduction [i] would yield (91, 251, 726)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 532704 423815 442258 496542 242900 256830 148862 597705 128031 699841 983165 682287 525579 222630 097634 117535 290269 351469 649317 225560 209873 674091 412312 837905 066179 > 4²⁵¹ [i]