MinT - Best Known (117, 252, s)-Nets in Base 4

Best Known (117, 252, s)-Nets in Base 4

(117, 252, 130)-Net over F₄ — Constructive and digital

Digital (117, 252, 130)-net over F₄, using

t-expansion [i] based on digital (105, 252, 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]

(117, 252, 168)-Net over F₄ — Digital

Digital (117, 252, 168)-net over F₄, using

t-expansion [i] based on digital (115, 252, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(117, 252, 1493)-Net in Base 4 — Upper bound on s

There is no (117, 252, 1494)-net in base 4, because

1 times m-reduction [i] would yield (117, 251, 1494)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 519511 573512 713640 494651 617439 902584 432730 488937 561431 625565 516488 508584 261966 587997 791801 999070 701112 449220 795526 113870 960287 811542 645216 069048 304530 > 4²⁵¹ [i]