MinT - Best Known (80, 114, s)-Nets in Base 4

Best Known (80, 114, s)-Nets in Base 4

(80, 114, 312)-Net over F₄ — Constructive and digital

Digital (80, 114, 312)-net over F₄, using

t-expansion [i] based on digital (79, 114, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 38, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(80, 114, 544)-Net over F₄ — Digital

Digital (80, 114, 544)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 114, 26057)-Net in Base 4 — Upper bound on s

There is no (80, 114, 26058)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 431 381525 642185 606554 215396 768921 293802 839001 761635 860226 329357 085844 > 4¹¹⁴ [i]