MinT - Best Known (161, 161+52, s)-Nets in Base 4

Best Known (161, 161+52, s)-Nets in Base 4

(161, 161+52, 1032)-Net over F₄ — Constructive and digital

Digital (161, 213, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (160, 212, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 53, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(161, 161+52, 2189)-Net over F₄ — Digital

Digital (161, 213, 2189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 161+52, 300885)-Net in Base 4 — Upper bound on s

There is no (161, 213, 300886)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 173 292349 822047 382530 647478 253628 710930 350204 897699 555928 247490 889156 343368 277108 665449 760299 249784 470139 438250 504584 847604 300496 > 4²¹³ [i]