MinT - Best Known (101, 101+131, s)-Nets in Base 4

Best Known (101, 101+131, s)-Nets in Base 4

(101, 101+131, 104)-Net over F₄ — Constructive and digital

Digital (101, 232, 104)-net over F₄, using

t-expansion [i] based on digital (73, 232, 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]

(101, 101+131, 144)-Net over F₄ — Digital

Digital (101, 232, 144)-net over F₄, using

t-expansion [i] based on digital (91, 232, 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]

(101, 101+131, 1098)-Net in Base 4 — Upper bound on s

There is no (101, 232, 1099)-net in base 4, because

1 times m-reduction [i] would yield (101, 231, 1099)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 146660 333768 099380 330409 266723 618687 041075 458453 170018 866314 573888 254932 172244 924188 649632 305767 506550 778857 512061 580700 388420 595033 091570 > 4²³¹ [i]