MinT - Best Known (118, 118+119, s)-Nets in Base 4

Best Known (118, 118+119, s)-Nets in Base 4

(118, 118+119, 130)-Net over F₄ — Constructive and digital

Digital (118, 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]

(118, 118+119, 168)-Net over F₄ — Digital

Digital (118, 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]

(118, 118+119, 1899)-Net in Base 4 — Upper bound on s

There is no (118, 237, 1900)-net in base 4, because

1 times m-reduction [i] would yield (118, 236, 1900)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12491 535492 156811 190635 488933 302892 622480 078228 676364 745216 268452 427681 546925 145847 232145 114331 462518 842783 251288 590830 457678 783169 175353 117356 > 4²³⁶ [i]