MinT - Best Known (194−100, 194, s)-Nets in Base 4

Best Known (194−100, 194, s)-Nets in Base 4

(194−100, 194, 104)-Net over F₄ — Constructive and digital

Digital (94, 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]

(194−100, 194, 144)-Net over F₄ — Digital

Digital (94, 194, 144)-net over F₄, using

t-expansion [i] based on digital (91, 194, 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]

(194−100, 194, 1367)-Net in Base 4 — Upper bound on s

There is no (94, 194, 1368)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 651 808355 947441 528943 560694 874163 593170 905632 424046 403624 228234 674124 438476 721475 647454 687361 957391 115508 483671 994986 > 4¹⁹⁴ [i]