MinT - Best Known (73, 73+79, s)-Nets in Base 4

Best Known (73, 73+79, s)-Nets in Base 4

(73, 73+79, 104)-Net over F₄ — Constructive and digital

Digital (73, 152, 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+79, 112)-Net over F₄ — Digital

Digital (73, 152, 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+79, 1068)-Net in Base 4 — Upper bound on s

There is no (73, 152, 1069)-net in base 4, because

1 times m-reduction [i] would yield (73, 151, 1069)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 8 364573 631090 000808 856983 390130 679887 210990 014153 370457 197124 411031 693191 705310 139279 059320 > 4¹⁵¹ [i]