MinT - Best Known (117, 117+125, s)-Nets in Base 4

Best Known (117, 117+125, s)-Nets in Base 4

(117, 117+125, 130)-Net over F₄ — Constructive and digital

Digital (117, 242, 130)-net over F₄, using

t-expansion [i] based on digital (105, 242, 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, 117+125, 168)-Net over F₄ — Digital

Digital (117, 242, 168)-net over F₄, using

t-expansion [i] based on digital (115, 242, 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, 117+125, 1695)-Net in Base 4 — Upper bound on s

There is no (117, 242, 1696)-net in base 4, because

1 times m-reduction [i] would yield (117, 241, 1696)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 579338 293399 613248 468733 167292 107309 432151 758944 943050 102168 678629 441365 354429 939350 436595 703779 524275 580652 258253 509488 563232 183952 281510 918588 > 4²⁴¹ [i]