MinT - Best Known (98, 98+137, s)-Nets in Base 4

Best Known (98, 98+137, s)-Nets in Base 4

(98, 98+137, 104)-Net over F₄ — Constructive and digital

Digital (98, 235, 104)-net over F₄, using

t-expansion [i] based on digital (73, 235, 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]

(98, 98+137, 144)-Net over F₄ — Digital

Digital (98, 235, 144)-net over F₄, using

t-expansion [i] based on digital (91, 235, 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]

(98, 98+137, 973)-Net in Base 4 — Upper bound on s

There is no (98, 235, 974)-net in base 4, because

1 times m-reduction [i] would yield (98, 234, 974)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 784 986915 554899 651411 397019 857252 651738 638470 991637 084450 326574 351254 753478 818328 766530 503182 842096 923904 830648 121329 294310 399526 714674 793625 > 4²³⁴ [i]