MinT - Best Known (181−101, 181, s)-Nets in Base 4

Best Known (181−101, 181, s)-Nets in Base 4

(181−101, 181, 104)-Net over F₄ — Constructive and digital

Digital (80, 181, 104)-net over F₄, using

t-expansion [i] based on digital (73, 181, 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]

(181−101, 181, 112)-Net over F₄ — Digital

Digital (80, 181, 112)-net over F₄, using

t-expansion [i] based on digital (73, 181, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(181−101, 181, 914)-Net in Base 4 — Upper bound on s

There is no (80, 181, 915)-net in base 4, because

1 times m-reduction [i] would yield (80, 180, 915)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 424345 076290 710941 655894 310941 861151 535092 787194 392155 537258 194605 180233 247052 521643 910368 537543 751222 017340 > 4¹⁸⁰ [i]