MinT - Best Known (96, 96+143, s)-Nets in Base 4

Best Known (96, 96+143, s)-Nets in Base 4

(96, 96+143, 104)-Net over F₄ — Constructive and digital

Digital (96, 239, 104)-net over F₄, using

t-expansion [i] based on digital (73, 239, 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]

(96, 96+143, 144)-Net over F₄ — Digital

Digital (96, 239, 144)-net over F₄, using

t-expansion [i] based on digital (91, 239, 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]

(96, 96+143, 890)-Net in Base 4 — Upper bound on s

There is no (96, 239, 891)-net in base 4, because

1 times m-reduction [i] would yield (96, 238, 891)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 204130 541495 859911 076701 283855 924676 319008 584160 677996 937050 455771 720903 190513 482524 420388 401170 008049 719052 803484 394802 555152 586378 759873 257216 > 4²³⁸ [i]