MinT - Best Known (80, 80+160, s)-Nets in Base 4

Best Known (80, 80+160, s)-Nets in Base 4

(80, 80+160, 104)-Net over F₄ — Constructive and digital

Digital (80, 240, 104)-net over F₄, using

t-expansion [i] based on digital (73, 240, 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]

(80, 80+160, 112)-Net over F₄ — Digital

Digital (80, 240, 112)-net over F₄, using

t-expansion [i] based on digital (73, 240, 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]

(80, 80+160, 589)-Net in Base 4 — Upper bound on s

There is no (80, 240, 590)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 526918 028171 810868 833336 866132 795656 042198 383227 949050 792684 910534 289177 737056 635940 817484 198256 483102 277614 218856 342352 782151 846418 476757 124000 > 4²⁴⁰ [i]