MinT - Best Known (194−114, 194, s)-Nets in Base 4

Best Known (194−114, 194, s)-Nets in Base 4

(194−114, 194, 104)-Net over F₄ — Constructive and digital

Digital (80, 194, 104)-net over F₄, using

t-expansion [i] based on digital (73, 194, 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]

(194−114, 194, 112)-Net over F₄ — Digital

Digital (80, 194, 112)-net over F₄, using

t-expansion [i] based on digital (73, 194, 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]

(194−114, 194, 778)-Net in Base 4 — Upper bound on s

There is no (80, 194, 779)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 670 245809 355478 648693 834020 068166 042403 167242 969606 559796 164833 305938 210510 534933 454576 563096 994454 973636 315059 677600 > 4¹⁹⁴ [i]