MinT - Best Known (190−98, 190, s)-Nets in Base 4

Best Known (190−98, 190, s)-Nets in Base 4

(190−98, 190, 104)-Net over F₄ — Constructive and digital

Digital (92, 190, 104)-net over F₄, using

t-expansion [i] based on digital (73, 190, 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]

(190−98, 190, 144)-Net over F₄ — Digital

Digital (92, 190, 144)-net over F₄, using

t-expansion [i] based on digital (91, 190, 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]

(190−98, 190, 1336)-Net in Base 4 — Upper bound on s

There is no (92, 190, 1337)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 516925 848462 047447 664010 188537 483012 379047 642243 510570 861935 266613 999066 536063 081461 100669 080363 067211 014125 619412 > 4¹⁹⁰ [i]