MinT - Best Known (234−113, 234, s)-Nets in Base 4

Best Known (234−113, 234, s)-Nets in Base 4

(234−113, 234, 130)-Net over F₄ — Constructive and digital

Digital (121, 234, 130)-net over F₄, using

t-expansion [i] based on digital (105, 234, 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]

(234−113, 234, 184)-Net over F₄ — Digital

Digital (121, 234, 184)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−113, 234, 2269)-Net in Base 4 — Upper bound on s

There is no (121, 234, 2270)-net in base 4, because

1 times m-reduction [i] would yield (121, 233, 2270)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195 152550 471925 824767 559354 112255 361356 458522 131654 868407 289115 872145 751610 597779 438548 759456 110121 331028 093624 186512 286774 256585 630817 686618 > 4²³³ [i]