MinT - Best Known (93, 93+145, s)-Nets in Base 4

Best Known (93, 93+145, s)-Nets in Base 4

(93, 93+145, 104)-Net over F₄ — Constructive and digital

Digital (93, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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]

(93, 93+145, 144)-Net over F₄ — Digital

Digital (93, 238, 144)-net over F₄, using

t-expansion [i] based on digital (91, 238, 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]

(93, 93+145, 825)-Net in Base 4 — Upper bound on s

There is no (93, 238, 826)-net in base 4, because

1 times m-reduction [i] would yield (93, 237, 826)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51420 768533 731797 349834 941536 380596 999147 983789 538312 010341 560862 980564 610896 381724 079241 237315 648655 591347 984723 742542 894842 429706 820842 232580 > 4²³⁷ [i]