MinT - Best Known (137, 137+113, s)-Nets in Base 4

Best Known (137, 137+113, s)-Nets in Base 4

(137, 137+113, 130)-Net over F₄ — Constructive and digital

Digital (137, 250, 130)-net over F₄, using

t-expansion [i] based on digital (105, 250, 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]

(137, 137+113, 241)-Net over F₄ — Digital

Digital (137, 250, 241)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+113, 3393)-Net in Base 4 — Upper bound on s

There is no (137, 250, 3394)-net in base 4, because

1 times m-reduction [i] would yield (137, 249, 3394)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 819803 118060 624160 985742 176337 370242 149496 910561 520141 309074 607458 424439 428700 863370 779586 787498 625820 452178 664986 504534 070019 515748 171582 927577 234904 > 4²⁴⁹ [i]