MinT - Best Known (235−162, 235, s)-Nets in Base 4

Best Known (235−162, 235, s)-Nets in Base 4

(235−162, 235, 104)-Net over F₄ — Constructive and digital

Digital (73, 235, 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]

(235−162, 235, 112)-Net over F₄ — Digital

Digital (73, 235, 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]

(235−162, 235, 511)-Net in Base 4 — Upper bound on s

There is no (73, 235, 512)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3089 659119 396580 214762 768668 539706 414216 984121 200703 476943 534336 720664 065015 992584 776879 560812 387350 718530 758133 068488 153675 938201 655527 074825 > 4²³⁵ [i]