MinT - Best Known (125, 222, s)-Nets in Base 4

Best Known (125, 222, s)-Nets in Base 4

(125, 222, 130)-Net over F₄ — Constructive and digital

Digital (125, 222, 130)-net over F₄, using

t-expansion [i] based on digital (105, 222, 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]

(125, 222, 241)-Net over F₄ — Digital

Digital (125, 222, 241)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(125, 222, 3655)-Net in Base 4 — Upper bound on s

There is no (125, 222, 3656)-net in base 4, because

1 times m-reduction [i] would yield (125, 221, 3656)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 358443 097855 189410 924027 426351 117063 831836 864080 824641 689500 661203 016162 849255 296101 683790 829594 915587 747555 329017 928273 837888 206092 > 4²²¹ [i]