MinT - Best Known (251−123, 251, s)-Nets in Base 4

Best Known (251−123, 251, s)-Nets in Base 4

(251−123, 251, 130)-Net over F₄ — Constructive and digital

Digital (128, 251, 130)-net over F₄, using

t-expansion [i] based on digital (105, 251, 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]

(251−123, 251, 187)-Net over F₄ — Digital

Digital (128, 251, 187)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−123, 251, 2254)-Net in Base 4 — Upper bound on s

There is no (128, 251, 2255)-net in base 4, because

1 times m-reduction [i] would yield (128, 250, 2255)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 318009 442646 711302 219574 037486 282678 620740 404420 188183 329218 946877 063695 899649 967790 560695 220195 698151 599107 135158 799439 962180 175954 039875 602249 373736 > 4²⁵⁰ [i]