MinT - Best Known (97, 97+159, s)-Nets in Base 4

Best Known (97, 97+159, s)-Nets in Base 4

(97, 97+159, 104)-Net over F₄ — Constructive and digital

Digital (97, 256, 104)-net over F₄, using

t-expansion [i] based on digital (73, 256, 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]

(97, 97+159, 144)-Net over F₄ — Digital

Digital (97, 256, 144)-net over F₄, using

t-expansion [i] based on digital (91, 256, 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]

(97, 97+159, 820)-Net in Base 4 — Upper bound on s

There is no (97, 256, 821)-net in base 4, because

1 times m-reduction [i] would yield (97, 255, 821)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3407 588214 140748 556272 359117 115472 056705 090715 873774 247426 224913 536768 449895 669268 628604 995344 939784 468940 732059 980625 968614 600732 922898 415009 298066 098240 > 4²⁵⁵ [i]