MinT - Best Known (242−146, 242, s)-Nets in Base 4

Best Known (242−146, 242, s)-Nets in Base 4

(242−146, 242, 104)-Net over F₄ — Constructive and digital

Digital (96, 242, 104)-net over F₄, using

t-expansion [i] based on digital (73, 242, 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]

(242−146, 242, 144)-Net over F₄ — Digital

Digital (96, 242, 144)-net over F₄, using

t-expansion [i] based on digital (91, 242, 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]

(242−146, 242, 865)-Net in Base 4 — Upper bound on s

There is no (96, 242, 866)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 50 559716 600554 312698 017664 797961 977386 720803 699832 149990 607840 438977 142351 775219 724644 338426 890986 239119 968616 372681 983145 253674 769395 001723 895116 > 4²⁴² [i]