MinT - Best Known (206−121, 206, s)-Nets in Base 4

Best Known (206−121, 206, s)-Nets in Base 4

(206−121, 206, 104)-Net over F₄ — Constructive and digital

Digital (85, 206, 104)-net over F₄, using

t-expansion [i] based on digital (73, 206, 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]

(206−121, 206, 129)-Net over F₄ — Digital

Digital (85, 206, 129)-net over F₄, using

t-expansion [i] based on digital (81, 206, 129)-net over F₄, using
- net from sequence [i] based on digital (81, 128)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
    - Drinfeld modules of rank 1 [i]

(206−121, 206, 833)-Net in Base 4 — Upper bound on s

There is no (85, 206, 834)-net in base 4, because

1 times m-reduction [i] would yield (85, 205, 834)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2812 440640 570485 284353 150719 327653 735160 726134 632884 136509 175272 734641 340352 364044 200472 989375 803839 962077 417748 562355 886320 > 4²⁰⁵ [i]