MinT - Best Known (232−140, 232, s)-Nets in Base 4

Best Known (232−140, 232, s)-Nets in Base 4

(232−140, 232, 104)-Net over F₄ — Constructive and digital

Digital (92, 232, 104)-net over F₄, using

t-expansion [i] based on digital (73, 232, 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]

(232−140, 232, 144)-Net over F₄ — Digital

Digital (92, 232, 144)-net over F₄, using

t-expansion [i] based on digital (91, 232, 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]

(232−140, 232, 830)-Net in Base 4 — Upper bound on s

There is no (92, 232, 831)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48 965682 972752 521626 492247 815541 544127 669230 344415 517139 771058 563059 313691 251305 312782 807086 722443 265132 200761 871215 022078 573525 032997 001940 > 4²³² [i]