MinT - Best Known (237−133, 237, s)-Nets in Base 4

Best Known (237−133, 237, s)-Nets in Base 4

(237−133, 237, 104)-Net over F₄ — Constructive and digital

Digital (104, 237, 104)-net over F₄, using

t-expansion [i] based on digital (73, 237, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(237−133, 237, 144)-Net over F₄ — Digital

Digital (104, 237, 144)-net over F₄, using

t-expansion [i] based on digital (91, 237, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(237−133, 237, 1150)-Net in Base 4 — Upper bound on s

There is no (104, 237, 1151)-net in base 4, because

1 times m-reduction [i] would yield (104, 236, 1151)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12282 565181 023732 421761 024599 423723 978161 311809 075254 078129 541773 571797 191724 850186 603157 188160 388452 512403 035693 520412 280038 741460 833651 227585 > 4²³⁶ [i]