MinT - Best Known (108, 108+115, s)-Nets in Base 4

Best Known (108, 108+115, s)-Nets in Base 4

(108, 108+115, 130)-Net over F₄ — Constructive and digital

Digital (108, 223, 130)-net over F₄, using

t-expansion [i] based on digital (105, 223, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(108, 108+115, 144)-Net over F₄ — Digital

Digital (108, 223, 144)-net over F₄, using

t-expansion [i] based on digital (91, 223, 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]

(108, 108+115, 1581)-Net in Base 4 — Upper bound on s

There is no (108, 223, 1582)-net in base 4, because

1 times m-reduction [i] would yield (108, 222, 1582)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 699065 710441 237641 212256 619114 587601 853941 249108 119025 657222 300343 146276 410428 065219 920061 589817 811012 775648 015368 331144 947610 788000 > 4²²² [i]