MinT - Best Known (73, 73+103, s)-Nets in Base 4

Best Known (73, 73+103, s)-Nets in Base 4

(73, 73+103, 104)-Net over F₄ — Constructive and digital

Digital (73, 176, 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, 73+103, 112)-Net over F₄ — Digital

Digital (73, 176, 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, 73+103, 729)-Net in Base 4 — Upper bound on s

There is no (73, 176, 730)-net in base 4, because

1 times m-reduction [i] would yield (73, 175, 730)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2435 578336 111582 558206 477068 942503 947926 471272 784157 914223 326529 475677 075772 892435 423332 038252 075099 457816 > 4¹⁷⁵ [i]