MinT - Best Known (103, 103+149, s)-Nets in Base 4

Best Known (103, 103+149, s)-Nets in Base 4

(103, 103+149, 104)-Net over F₄ — Constructive and digital

Digital (103, 252, 104)-net over F₄, using

t-expansion [i] based on digital (73, 252, 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]

(103, 103+149, 144)-Net over F₄ — Digital

Digital (103, 252, 144)-net over F₄, using

t-expansion [i] based on digital (91, 252, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(103, 103+149, 982)-Net in Base 4 — Upper bound on s

There is no (103, 252, 983)-net in base 4, because

1 times m-reduction [i] would yield (103, 251, 983)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 661139 771838 732818 746613 744632 383567 661729 171358 851626 431922 274598 642822 466098 953375 659941 797471 180299 074256 750236 236903 039544 764596 519085 958154 537354 > 4²⁵¹ [i]