MinT - Best Known (180, 180+58, s)-Nets in Base 4

Best Known (180, 180+58, s)-Nets in Base 4

(180, 180+58, 1032)-Net over F₄ — Constructive and digital

Digital (180, 238, 1032)-net over F₄, using

4² times duplication [i] based on digital (178, 236, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 59, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(180, 180+58, 2431)-Net over F₄ — Digital

Digital (180, 238, 2431)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+58, 339636)-Net in Base 4 — Upper bound on s

There is no (180, 238, 339637)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 195114 711363 294152 687598 382679 419148 689071 107167 298184 595529 757928 541659 057016 111323 029270 741160 386687 071136 907938 618589 303514 105356 574125 474096 > 4²³⁸ [i]