MinT - Best Known (245−151, 245, s)-Nets in Base 4

Best Known (245−151, 245, s)-Nets in Base 4

(245−151, 245, 104)-Net over F₄ — Constructive and digital

Digital (94, 245, 104)-net over F₄, using

t-expansion [i] based on digital (73, 245, 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]

(245−151, 245, 144)-Net over F₄ — Digital

Digital (94, 245, 144)-net over F₄, using

t-expansion [i] based on digital (91, 245, 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]

(245−151, 245, 810)-Net in Base 4 — Upper bound on s

There is no (94, 245, 811)-net in base 4, because

1 times m-reduction [i] would yield (94, 244, 811)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 803 438546 953764 127149 900479 536693 123889 754692 216179 055180 786727 203633 500355 517188 548178 197954 352744 874308 783872 850000 658351 620086 566547 122594 931600 > 4²⁴⁴ [i]