MinT - Best Known (238−121, 238, s)-Nets in Base 4

Best Known (238−121, 238, s)-Nets in Base 4

(238−121, 238, 130)-Net over F₄ — Constructive and digital

Digital (117, 238, 130)-net over F₄, using

t-expansion [i] based on digital (105, 238, 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]

(238−121, 238, 168)-Net over F₄ — Digital

Digital (117, 238, 168)-net over F₄, using

t-expansion [i] based on digital (115, 238, 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]

(238−121, 238, 1797)-Net in Base 4 — Upper bound on s

There is no (117, 238, 1798)-net in base 4, because

1 times m-reduction [i] would yield (117, 237, 1798)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49558 265681 316034 552979 826848 795311 624112 382002 867252 371952 898656 602629 901767 971474 072204 668234 840739 342732 949470 664860 011582 699645 589892 877600 > 4²³⁷ [i]