MinT - Best Known (220−72, 220, s)-Nets in Base 4

Best Known (220−72, 220, s)-Nets in Base 4

(220−72, 220, 240)-Net over F₄ — Constructive and digital

Digital (148, 220, 240)-net over F₄, using

4¹ times duplication [i] based on digital (147, 219, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 73, 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]

(220−72, 220, 640)-Net over F₄ — Digital

Digital (148, 220, 640)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(220−72, 220, 22714)-Net in Base 4 — Upper bound on s

There is no (148, 220, 22715)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 840338 625078 832261 335324 255909 016434 752116 417748 851839 339503 808732 226086 346904 581867 979548 600156 728688 821298 409337 583531 212425 115914 > 4²²⁰ [i]