MinT - Best Known (78, 238, s)-Nets in Base 4

Best Known (78, 238, s)-Nets in Base 4

(78, 238, 104)-Net over F₄ — Constructive and digital

Digital (78, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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]

(78, 238, 112)-Net over F₄ — Digital

Digital (78, 238, 112)-net over F₄, using

t-expansion [i] based on digital (73, 238, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(78, 238, 566)-Net in Base 4 — Upper bound on s

There is no (78, 238, 567)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 198781 457303 493214 298746 606525 520910 598466 016813 656200 393127 000954 426833 669810 456378 028602 363574 097760 887269 098574 935588 055542 693925 684082 718360 > 4²³⁸ [i]