MinT - Best Known (73, 179, s)-Nets in Base 4

Best Known (73, 179, s)-Nets in Base 4

(73, 179, 104)-Net over F₄ — Constructive and digital

Digital (73, 179, 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]

(73, 179, 112)-Net over F₄ — Digital

Digital (73, 179, 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]

(73, 179, 698)-Net in Base 4 — Upper bound on s

There is no (73, 179, 699)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 601183 082642 831273 027359 117777 932067 127337 981845 292377 187456 727547 809024 625324 072994 672874 938445 715107 302676 > 4¹⁷⁹ [i]