MinT - Best Known (81, 81+120, s)-Nets in Base 4

Best Known (81, 81+120, s)-Nets in Base 4

(81, 81+120, 104)-Net over F₄ — Constructive and digital

Digital (81, 201, 104)-net over F₄, using

t-expansion [i] based on digital (73, 201, 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]

(81, 81+120, 129)-Net over F₄ — Digital

Digital (81, 201, 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]

(81, 81+120, 755)-Net in Base 4 — Upper bound on s

There is no (81, 201, 756)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 827694 364853 107943 689775 116896 199549 910987 402204 576669 634466 168713 710718 947803 428230 270647 122495 842762 586896 807151 345360 > 4²⁰¹ [i]