MinT - Best Known (170−110, 170, s)-Nets in Base 4

Best Known (170−110, 170, s)-Nets in Base 4

(170−110, 170, 66)-Net over F₄ — Constructive and digital

Digital (60, 170, 66)-net over F₄, using

t-expansion [i] based on digital (49, 170, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(170−110, 170, 91)-Net over F₄ — Digital

Digital (60, 170, 91)-net over F₄, using

t-expansion [i] based on digital (50, 170, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(170−110, 170, 472)-Net in Base 4 — Upper bound on s

There is no (60, 170, 473)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 368181 242069 057719 244115 274109 714507 776398 124101 336026 184659 950563 641408 019633 050285 672630 171367 021200 > 4¹⁷⁰ [i]