MinT - Best Known (220−128, 220, s)-Nets in Base 4

Best Known (220−128, 220, s)-Nets in Base 4

(220−128, 220, 104)-Net over F₄ — Constructive and digital

Digital (92, 220, 104)-net over F₄, using

t-expansion [i] based on digital (73, 220, 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]

(220−128, 220, 144)-Net over F₄ — Digital

Digital (92, 220, 144)-net over F₄, using

t-expansion [i] based on digital (91, 220, 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]

(220−128, 220, 913)-Net in Base 4 — Upper bound on s

There is no (92, 220, 914)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 910600 857014 337329 895485 248551 102601 334249 561598 297196 866740 702574 329522 728510 238533 981286 383681 444309 204368 243401 764156 449227 818130 > 4²²⁰ [i]