MinT - Best Known (157−84, 157, s)-Nets in Base 4

Best Known (157−84, 157, s)-Nets in Base 4

(157−84, 157, 104)-Net over F₄ — Constructive and digital

Digital (73, 157, 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]

(157−84, 157, 112)-Net over F₄ — Digital

Digital (73, 157, 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]

(157−84, 157, 945)-Net in Base 4 — Upper bound on s

There is no (73, 157, 946)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 33397 415124 696566 203337 459510 113021 967861 990404 751067 606568 701207 571615 555121 104309 931033 345560 > 4¹⁵⁷ [i]