MinT - Best Known (128, 128+62, s)-Nets in Base 4

Best Known (128, 128+62, s)-Nets in Base 4

(128, 128+62, 240)-Net over F₄ — Constructive and digital

Digital (128, 190, 240)-net over F₄, using

4¹ times duplication [i] based on digital (127, 189, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 63, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(128, 128+62, 569)-Net over F₄ — Digital

Digital (128, 190, 569)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+62, 20249)-Net in Base 4 — Upper bound on s

There is no (128, 190, 20250)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 464547 223796 672394 910087 454452 175012 762316 471462 800598 041724 738428 115779 595861 180609 349075 654319 880022 460819 363456 > 4¹⁹⁰ [i]