MinT - Best Known (128, 223, s)-Nets in Base 4

Best Known (128, 223, s)-Nets in Base 4

(128, 223, 130)-Net over F₄ — Constructive and digital

Digital (128, 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]

(128, 223, 263)-Net over F₄ — Digital

Digital (128, 223, 263)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 223, 4234)-Net in Base 4 — Upper bound on s

There is no (128, 223, 4235)-net in base 4, because

1 times m-reduction [i] would yield (128, 222, 4235)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 606325 915153 758012 154519 385766 684944 220659 064606 616028 771366 727695 859481 021054 511064 155974 480793 477227 328945 286772 565242 774734 386944 > 4²²² [i]