MinT - Best Known (100, 100+111, s)-Nets in Base 4

Best Known (100, 100+111, s)-Nets in Base 4

(100, 100+111, 104)-Net over F₄ — Constructive and digital

Digital (100, 211, 104)-net over F₄, using

t-expansion [i] based on digital (73, 211, 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]

(100, 100+111, 144)-Net over F₄ — Digital

Digital (100, 211, 144)-net over F₄, using

t-expansion [i] based on digital (91, 211, 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]

(100, 100+111, 1370)-Net in Base 4 — Upper bound on s

There is no (100, 211, 1371)-net in base 4, because

1 times m-reduction [i] would yield (100, 210, 1371)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 772576 602969 747737 191320 739842 748449 471061 055814 047480 087135 642164 645830 036651 231829 956892 727262 672565 879084 093800 924631 205696 > 4²¹⁰ [i]