MinT - Best Known (237−121, 237, s)-Nets in Base 4

Best Known (237−121, 237, s)-Nets in Base 4

(237−121, 237, 130)-Net over F₄ — Constructive and digital

Digital (116, 237, 130)-net over F₄, using

t-expansion [i] based on digital (105, 237, 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]

(237−121, 237, 168)-Net over F₄ — Digital

Digital (116, 237, 168)-net over F₄, using

t-expansion [i] based on digital (115, 237, 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]

(237−121, 237, 1755)-Net in Base 4 — Upper bound on s

There is no (116, 237, 1756)-net in base 4, because

1 times m-reduction [i] would yield (116, 236, 1756)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12461 469547 481089 401003 182966 204995 307348 502784 754774 279207 957813 265839 523998 292302 058108 189271 166508 481129 128451 231636 475368 975511 530186 213360 > 4²³⁶ [i]