MinT - Best Known (253−155, 253, s)-Nets in Base 4

Best Known (253−155, 253, s)-Nets in Base 4

(253−155, 253, 104)-Net over F₄ — Constructive and digital

Digital (98, 253, 104)-net over F₄, using

t-expansion [i] based on digital (73, 253, 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]

(253−155, 253, 144)-Net over F₄ — Digital

Digital (98, 253, 144)-net over F₄, using

t-expansion [i] based on digital (91, 253, 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]

(253−155, 253, 856)-Net in Base 4 — Upper bound on s

There is no (98, 253, 857)-net in base 4, because

1 times m-reduction [i] would yield (98, 252, 857)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 56 660677 317067 619066 029869 866130 118955 032647 920747 986041 525209 899366 324099 967375 443558 758205 975506 606913 344116 325562 885652 230341 131246 032209 121483 335520 > 4²⁵² [i]