MinT - Best Known (73, 73+149, s)-Nets in Base 4

Best Known (73, 73+149, s)-Nets in Base 4

(73, 73+149, 104)-Net over F₄ — Constructive and digital

Digital (73, 222, 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+149, 112)-Net over F₄ — Digital

Digital (73, 222, 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+149, 535)-Net in Base 4 — Upper bound on s

There is no (73, 222, 536)-net in base 4, because

1 times m-reduction [i] would yield (73, 221, 536)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 464426 055259 140342 107140 733711 527567 421246 368644 400724 529894 209282 655990 588993 130943 161915 554967 561752 780276 279887 598137 222611 529200 > 4²²¹ [i]