MinT - Best Known (115, 115+137, s)-Nets in Base 4

Best Known (115, 115+137, s)-Nets in Base 4

(115, 115+137, 130)-Net over F₄ — Constructive and digital

Digital (115, 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]

(115, 115+137, 168)-Net over F₄ — Digital

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]

(115, 115+137, 1399)-Net in Base 4 — Upper bound on s

There is no (115, 252, 1400)-net in base 4, because

1 times m-reduction [i] would yield (115, 251, 1400)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13 542114 171523 227525 648387 942258 528560 310409 719016 091797 812809 460653 987472 288230 914746 750952 663460 775369 745590 944662 256549 874925 481909 769393 771834 692641 > 4²⁵¹ [i]